The invention relates to a method for reconstructing the source of an electromagnetic field. The invention also relates to an arrangement for carrying out the method.
According to the laws of electrodynamics, the characteristics of an electromagnetic field inside a closed spatial region can be determined exactly only when specific characteristics of the electromagnetic field are known on a surface completely surrounding the spatial region. Exact determinability is independent of whether or not there is a source of the electromagnetic field in the closed spatial region.
The laws of electrodynamics are based on the supposition of a continuous and gapless knowledge of the characteristics of the electromagnetic field on the surface completely surrounding the spatial region. In technical applications, this assumption is not regularly the case. When the characteristics of an electromagnetic field on a surface are being measured, a multiplicity of measurement sensors are arranged on the surface. The items of information obtained by the measurement sensors and relating to the characteristics of the electromagnetic field on the surface are discrete. Unique determination of the electromagnetic field in the spatial region is also possible on the basis of the discrete measured values but, otherwise than for continuous measured values, no longer in an exact fashion, but only within an error bound. When it is stated in technical applications that an electromagnetic field is being uniquely determined in a closed spatial region by the recording of measured values on the surface thereof, what is always meant is a unique determination in the context of the error bound.
Such measurements are carried out, for example, in order to determine the characteristics of an antenna. To this end, measurement sensors are uniformly distributed on a surface completely surrounding the antenna, for example, a spherical surface, and measured values relating to characteristics of the electromagnetic field emitted by the antenna are recorded. A mathematical model of the antenna is set up, and a field expansion of the electromagnetic field emitted by the antenna is carried out, the coefficients of the field expansion firstly being unknown. With the aid of a system of equations, the unknowns of the field expansion are related to the measured values recorded by the measurement sensors. By solving the system of equations, the characteristics of the antenna can be uniquely calculated within the error bound determined by the discreteness of the measured values (J. E. Hansen (ed.), Spherical Near-Field Antenna Measurements, Peter Peregrinus Ltd., 1988).
It is frequently impossible or attended by an excessive outlay to arrange measurement sensors on a surface completely surrounding the electromagnetic source. This holds, for example, for an antenna near field measurement on a circular cylindrical surface, in the case of which the measurement sensors are arranged for design reasons only on the cylinder envelope, but not on the top and bottom of the cylinder. It is helpful to measure the electromagnetic field as far as possible (for example on the cylinder envelope), and otherwise to proceed on the basis of estimates (for example at the bottom and top). Information relating to the electromagnetic field is then available from the measured values and the estimates, when taken together, for a closed surface surrounding the electromagnetic source. The emission characteristics of the antenna can be uniquely calculated in the context of the error bound caused by the discreteness of the measured values from this information. However, the effect of the estimates is a further inaccuracy, whose extent cannot be exactly determined (C. A. Balanis, Advanced Engineering Electromagnetics, John Wiley & Sons, 1989).
A surface not completely surrounding the sources exists, in particular, for measurements which are undertaken on the human body in the course of magnetoencephalography or magnetocardiography. In magnetoencephalography, the magnetic field around the head is measured, and the brain currents that are the source of the magnetic field are reconstructed. In the case of magnetocardiography, a similar attempt is made to deduce the causative heart currents from magnetic fields around the trunk. In both instances, measurement sensors will need to be arranged inside the human body in order to measure the magnetic field on a surface completely surrounding the source.
Proceeding from the prior art mentioned at the beginning, it is the object of the invention to propose a method and an arrangement for reconstructing the source of an electromagnetic field that are affected by a lesser uncertainty. The object is achieved by the features of the independent claims. Advantageous embodiments are to be found in the subclaims.